Area of triangles

key notes :

What is a Triangle?

A triangle is a polygon with three sides and three angles.

The area of a triangle means the amount of surface enclosed inside it.

Formulas for Area of a Triangle

(a) Using Base and Height

Area=1/2×Base×Height

• Base (b): Any one side of the triangle.
• Height (h): The perpendicular distance from the opposite vertex to the base.

✅ Example:
Base = 10 cm, Height = 6 cm

Area=1/2×10×6=30 cm²

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(b) Using Heron’s Formula (when all 3 sides are given)

If the sides are a,b,c

1. First find semi-perimeter (s):

s=(a+b+c)/2

2. Then,

Area=√s(s−a)(s−b)(s−c)

✅ Example:
Sides = 6 cm, 8 cm, 10 cm

s=(6+8+10)²=12

Area=√12(12−6)(12−8)(12−10)​=√12×6×4×2​=√576​=24cm²

Special Types of Triangles

Right-angled triangle: Area=12×(Perpendicular side)×(Base side)\text{Area} = \tfrac{1}{2} \times \text{(Perpendicular side)} \times \text{(Base side)}Area=21​×(Perpendicular side)×(Base side)

Equilateral triangle (all sides equal):
If side = aaa, Area=34×a2\text{Area} = \tfrac{\sqrt{3}}{4} \times a^2Area=43​​×a2

Important Points

• Always check that height is perpendicular to the base.
• If only sides are given, use Heron’s formula.
• The unit of area is always in square units (cm², m², etc.).

Practice Questions

1. Find the area of a triangle with base = 12 cm and height = 9 cm.
2. Find the area of a right triangle with legs 6 cm and 8 cm.
3. Use Heron’s formula to find the area of a triangle with sides 7 cm, 9 cm, and 12 cm.
4. Find the area of an equilateral triangle with side 10 cm.

Learn with an example

Let’s practice!🖊️